## Characterization of completions of unique factorization domains

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- by Raymond C. Heitmann PDF
- Trans. Amer. Math. Soc.
**337**(1993), 379-387 Request permission

## Abstract:

It is shown that a complete local ring is the completion of a unique factorization domain if and only if it is a field, a discrete valuation ring, or it has depth at least two and no element of its prime ring is a zerodivisor. It is also shown that the Normal Chain Conjecture is false and that there exist local noncatenary UFDs.## References

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## Additional Information

- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**337**(1993), 379-387 - MSC: Primary 13B35; Secondary 13C15, 13F15
- DOI: https://doi.org/10.1090/S0002-9947-1993-1102888-9
- MathSciNet review: 1102888